If we allow our leaders to impose more and more gun laws, soon we will be like the EU. Where no citizen has the right to protect their life, liberty and pursuit of happiness.

Hillary Clinton’s support for stronger gun-control laws has become the central theme of her bid to win the Democratic primary in Connecticut, the state where a deadly shooting at an elementary school sparked a national dialogue about firearms.

In her first public campaign stop in the state this year, Mrs. Clinton spoke Thursday at a Hartford YMCA about gun policy. The event included two people who lost family members when a gunman fatally shot 20 children and six adult staff members at Sandy Hook Elementary School in Newtown in 2012.

“It’s not just about Sandy Hook any more,” said Erica Smegielski,daughter of Sandy Hook principal Dawn Hochsprung, who died in the shooting. “What we need to focus on is the everyday gun violence that plagues our cities and plagues our towns. We need to find a way to stop that.”

Mrs. Clinton, speaking ahead of the Connecticut primary Tuesday, said she would work to change the “gun culture” if elected president.

“We can do this consistent with the Second Amendment. We can do this with the support of responsible gun voters,” Mrs. Clinton said. “And that is exactly what we will do.”

Mrs. Clinton and her opponent for the Democratic nomination, Vermont Sen. Bernie Sanders, have been at odds over gun policy during the party’s nominating contests. Mr. Sanders, who represents the rural state of Vermont, has taken a more conservative stance on gun laws and has been fending off criticism from Mrs. Clinton.

Mr. Sanders’s campaign didn’t return requests for comment Thursday.

For Mrs. Clinton, gun policy is “the one issue where she can point to and say she is to the left of Bernie Sanders,” said Douglas Schwartz,director of the Quinnipiac University Poll.